x^2-18x=31

Solution for x^2-18x=31 equation:

x^2-18x=31

We move all terms to the left:

x^2-18x-(31)=0

a = 1; b = -18; c = -31;
Δ = b2-4ac
Δ = -182-4·1·(-31)
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-8\sqrt{7}}{2*1}=\frac{18-8\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+8\sqrt{7}}{2*1}=\frac{18+8\sqrt{7}}{2}
$